A control system of this kind has been proposed in Patent Literature 1 by the present applicant. This control system controls the air-fuel ratio of a mixture supplied to an internal combustion engine, and is comprised of an oxygen concentration sensor, a state predictor, and a DSM controller. In the control system, a predicted value PREVO2 of the difference between the output of the oxygen concentration sensor and a predetermined value is calculated by the state predictor, and inputted to the DSM controller to thereby calculate a target air-fuel ratio KCMD, and a fuel injection amount is calculated according to the target air-fuel ratio KCMD. The air-fuel ratio of a mixture supplied to the internal combustion engine is controlled using the fuel injection amount.
The DSM controller calculates the target air-fuel ratio KCMD according to the predicted value PREVO2 with a control algorithm to which is applied a ΔΣ modulation algorithm, and the control algorithm is expressed specifically by the following equations (a) to (g):r(k)=−1·G·PREVO2(k)  (a)r1(k)=sat(r(k))  (b)δ(k)=r1(k)−u″(k−1)  (c)σ(k)=σ(k−1)+δ(k)  (d)u″(k)=sgn(σ(k))  (e)u(k)=F·u″(k)  (f)KCMD(k)=FLAFBASE+FLAFADP+u(k)  (g)
wherein r(k) represents a reference input, u″ (k) a modulation output, and G and F gains. Further, sat(r(k)) represents a saturation function. The value of sat(r(k)) is set such that when r(k)<−1, sat(r(k))=−1 holds, when −1≦r (k)≦1, sat(r(k))=r(k) holds, and when r(k)>1, sat(r(k))=1 holds. Further, sgn(σ(k)) represents a sign function. The value of sgn(σ(k)) is set such that when σ(k)≧0, sgn(σ(k))=1 holds, and when σ(k)<0, sgn(σ(k))=−1 holds.
As described above, in the control algorithm, the reference input r(k) is limited by the saturation function sat(r(k)) such that the absolute value thereof becomes not larger than a value of 1, and the modulation output u″ (k) is calculated based on the limited value r1(k) thus limited, with the ΔΣ modulation algorithm of the equations (c) to (e). This is for the following reason: When the reference input r(k) is applied to the ΔΣ modulation algorithm without being limited as described above, if the absolute value of the reference input r(k) is larger than a value of 1, the absolute value of an integral value σ(k) of the difference δ (k) increases, whereby even when the sign (positive or negative) of the difference δ (k) is inverted in accordance with inversion of the sign of the reference input r(k), the sign of the modulation output u″ (k) is maintained without being inverted until the increased absolute value of the integral value σ(k) decreases. That is, a dead time is generated between the inversion of the sign of the reference input r(k) and the inversion of the sign of the modulation output u″ (k), which results in the degraded controllability. Therefore, the modulation output u″ (k) is calculated as described above in order to avoid such inconvenience.
[Patent Literature 1] Japanese Laid-Open Patent Publication (Kokai) No. 2004-70820
As in the above-described conventional control system, when the control input to the controlled object is calculated using the modulation output u″ (k) the sign of which is frequently inverted due to the characteristics of the ΔΣ modulation algorithm, the accuracy of control is higher as the ratio between respective frequencies of the inversion of the modulation output u″ (k) to a value of 1 and the inversion thereof to a value of −1 is closer to half and half. In other words, as the frequency of the inversion is smaller and a time period over which the modulation output u″ (k) is held at one of a value of 1 and a value of −1 becomes longer, the accuracy of the control becomes lower. In the above-described control system, the reference input r(k) for control of the air-fuel ratio is set such that the absolute value thereof becomes equal to a value close to 1 (equivalent ratio corresponding to the stoichiometric air-fuel ratio), and therefore a state does not frequently occur in which the frequency of the inversion of the modulation output u″ (k) is small and at the same time the modulation output u″ (k) is held at one of a value of 1 and a value of −1 for a long time. However, the input value to the ΔΣ modulation algorithm sometimes assumes only one of the positive value and the negative value depending on the characteristics of the controlled object. In such a case, the time period over which the modulation output u″ (k) is held at one of a value of 1 and a value of −1 becomes longer. Also, depending on the characteristics of the controlled object, a state in which the absolute value of the reference input r(k) input to the ΔΣ modulation algorithm is larger than a value of 1 sometimes continues for a long time. When such a controlled object is controlled by the above-described conventional control system, the limited value r1(k) is held at a value of 1 or a value of −1 for a long time, which causes the difference δ (k) and the integral value σ(k) to be held at the same value for a long time. In these cases, the switching behavior (inverting behavior) of the modulation output u″ which characterizes the ΔΣ modulation algorithm, is lost to reduce the frequency of the inversion of the modulation output u″ and hold the modulation output u″ at one of a value of 1 and a value of −1 for a longer time. This can result in the degraded accuracy of the control. This problem similarly occurs even when the Δ modulation algorithm or the ΣΔ modulation algorithm is used in place of the ΔΣ modulation algorithm.
The present invention has been made to provide a solution to the above-described problems, and a first object thereof is to provide a control system which is capable of enhancing the accuracy of control when the output of a controlled object is controlled with a control algorithm to which is applied a modulation algorithm based on one of a Δ modulation algorithm, a ΔΣ modulation algorithm, and a ΣΔ modulation algorithm, even if the absolute value of an input value to the control algorithm continue to be held larger than a value of 1 for a long time.
A second object of the present invention is to provide a control system which is capable of enhancing the accuracy of control when a controlled object is controlled with a control algorithm based on one of a Δ modulation algorithm, a ΔΣ modulation algorithm, and a ΣΔ modulation algorithm, even if an input value to the control algorithm assumes only one of a positive value and a negative value.